Grade 2 Module 5

Addition and Subtraction Within 1,000

with Word Problems to 100 OVERVIEW

In Module 4, students developed addition and subtraction fluency within 100 and began developing conceptual

understanding of the standard algorithm via place value strategies. In Module 5, students build upon their mas-

tery of renaming place value units and extend their work with conceptual understanding of the addition and sub-

traction algorithms to numbers within 1,000, always with the option of modeling with materials or drawings.

Throughout the module, students continue to focus on strengthening and deepening conceptual understanding

and fluency.

Topic A focuses on place value strategies to add and subtract within 1,000. Students relate 100 more and 100 less

to addition and subtraction of 100. They add and subtract multiples of 100, including counting on to subtract

(e.g., for 650 – 300, they start at 300 and think, “300 more gets me to 600, and 50 more gets me to 650, so…

350”). Students also use simplifying strategies for addition and subtraction: they extend the make a ten strategy

to make a hundred, mentally decomposing one addend to make a hundred with the other (e.g., 299 + 6 becomes

299 + 1 + 5, or 300 + 5, which equals 305) and use compensation to subtract from three-digit numbers (e.g., for

376 – 59, add 1 to each, 377 – 60 = 317). The topic ends with students sharing and critiquing solution strategies

for addition and subtraction problems. Throughout the topic, students use place value language and properties

of operations to explain why their strategies work.

In Topics B and C, students continue to build on Module 4’s work, now composing and decomposing tens and

hundreds within 1,000. As each of these topics begins, students relate manipulative representations to the algo-

rithm, then transition to making math drawings in place of the manipulatives. As always, students use place value

reasoning and properties of operations to explain their work.

Throughout Module 5, students maintain addition and subtraction fluency within 100 as they use these skills dur-

ing their daily application work to solve one- and two-step word problems of all types. The focus of concept de-

velopment is reserved for adding and subtracting within 1,000; using concrete models or drawings and strategies

based on place value, properties of operations, and/or the relationship between addition and subtraction; and

relating strategies to a written method. Note that a written method can include number bonds, chip models, ar-

row notation, the algorithm, or tape diagrams. Many students will need to record these strategies in order to

solve correctly. The lessons are designed to provide ample time for discussions that center on student reasoning,

explaining why their addition and subtraction strategies work. For example, students may use the relationship

between addition and subtraction to demonstrate why their subtraction solution is correct.

The module culminates with Topic D, wherein students synthesize their understanding of addition and subtrac-

tion strategies and choose which strategy is most efficient for given problems. They defend their choices using

place value language and their understanding of the properties of operations.

Terminology

Terminology

New or Recently Introduced Terms

Algorithm (a step-by-step procedure to solve a particular type of problem)

Compensation (simplifying strategy where students add or subtract the same amount to or from both numbers to

create an equivalent but easier problem)

Compose (e.g., to make 1 larger unit from 10 smaller units)

Decompose (e.g., to break 1 larger unit into 10 smaller units)

New groups below (show newly composed units on the line below the appropriate place in the addition algorithm)

Simplifying strategy (e.g., to solve 299 + 6, think 299 + 1 + 5 = 300 + 5 = 305.)

Familiar Terms and Symbols

Addend

Addition

Bundle

Difference

Equation

Number bond

Place value

Place value chart (pictured right)

Place value or number disk (pictured above right

Rename

Subtraction

Tape diagram

Total

Unbundle

Units of ones, tens, hundreds

Suggested Tools and Representations

Arrow notation, arrow way

Chip model (pictured right)

Number bond

Place value charts and mats (pictured above right)

Place value disk sets (18 ones, 18 tens, 18 hundreds, 1 one thousand per set)

Tape diagram

Lesson 1

Objective: Relate 10 more, 10 less, 100 more, and 100 less to addition and

subtraction of 10 and 100.

We add and subtract like units. The digit in the hundreds place changes when adding and subtracting 100, just as the

digit in the tens place changes when adding or subtracting 10.

The Arrow Method

Lesson 2

Objective: Add and subtract multiples of 100 including counting on to subtract.

Lesson 3

Objective: Add multiples of 100 and some tens within 1,000.

Lesson 4

Objective: Subtract multiples of 100 and some tens within 1,000.

When we subtract using mental math strategies it helps to use benchmark numbers.

440 — 260 =

Lesson 5

Objective: Use the associative property to make a hundred in one addend.

A mental math strategy is to take from one addend and give to the other so that

you have an even hundred.

Lesson 6

Objective: Use the associative property to subtract from three-digit numbers and

verify solutions with addition.

It is easier to subtract round numbers. Adding the same amount to the

minuend and the subtrahend will not effect the difference.

.

Lesson 7

Objective: Share and critique strategies for varied addition and subtraction prob-

lems within 1,000.

Students have a variety of strate-

gies to solve problems. Some

lend themselves better to specific

problems.

Lesson 8

Objective: Relate manipulative representations to the addition algorithm.

.

100 100 100 100

10 10

10 10 1 1 1 1 1

1 1 1

1 1

10

Lesson 9

Objective: Relate manipulative representations to the addition algorithm.

Lesson 10

Objective: Use math drawings to represent additions with up to two

compositions and relate drawings to the addition algorithm.

Lesson 11

Objective: Use math drawings to represent additions with up to two

compositions and relate drawings to the addition algorithm.

Lesson 12

Objective: Choose and

explain solution strategies

and record with a written

addition method.

Lesson 13

Objective: Relate manipulative representations to the subtraction algorithm, and

use addition to explain why the subtraction method works.

Lesson 14

Objective: Use math drawings to represent subtraction with up to two decompo-

sitions, relate drawings to the algorithm, and use addition to explain why the

subtraction method works.

Lesson 15

Objective: Use math drawings to represent subtraction with up to two decompo-

sitions, relate drawings to the algorithm, and use addition to explain why the

subtraction method works.

Lesson 16

Objective: Subtract from multiples of 100 and from numbers with zero in the

tens place.

Lesson 17

Objective: Subtract from multiples of 100 and from numbers with zero in the

tens place.

Lesson 18

Objective: Apply and explain alternate methods for sub-

tracting from multiples of 100 and from numbers with zero

in the tens place.

Using compensation helps us avoid having to subtract

across two or more zeros.

We can use the arrow method and our knowledge of addition to find the solu-

tion to a subtraction problem.

Lesson 19

Objective: Choose and explain solution strategies and record with a written addi-

tion or subtraction method.

Lesson 20

Objective: Choose and explain solution strategies and record with a written addi-

tion or subtraction method.

Compensation

Chip Model

Number Bond

Standard Algorithm

The Arrow Method

I used compensation and add-

ed 3 to both numbers, so that

I could subtract 300 instead of

297. So, 549 minus 300 equals

249. Easy!

I used a number bond since

499 is so close to 500. I

took 1 from 166 and added

it to 499 to get 500; then I

added on the rest to get

665.

I used the arrow way, because it’s easy to

add on from 499. I added on a hundred,

then 1 more to make 600, then 65 more. So,

I also got 665.

I used the algorithm

to solve, because I

know the steps, so it

doesn’t take me

long.